Spin Noise in Birefringent Media

It is known that linear birefringence of the medium essentially hinders measuring the Faraday effect. For this reason, optically anisotropic materials have never been considered as objects of the Faraday-rotation-based spin noise spectroscopy. We show, both theoretically and experimentally, that strong optical anisotropy that may badly suppress the regular Faraday rotation of the medium, practically does not affect the measurement of the spatially uncorrelated spin fluctuations. We also show that the birefringent media provide additional opportunity to measure spatial spin correlations. Results of the experimental measurements of the spin-noise spectra performed on ${\mathrm{Nd}}^{3+}$ ions in the uniaxial crystal matrices well agree with the theory.

Figure 1

Schematic presentation of the Stokes vector fluctuations for the light transmitted through a birefringent crystal. The axis ${\xi }_3$ corresponds to the polarizations along the main axes. The points $A$, $B$, and $C$, on the surface of the Poincaré sphere correspond to azimuths of the incident light polarization $\theta$ equal to $\pi /4$, approximately $\pi /8$, and 0. Conversion of the arc segment at $A$ to the round spot at $C$ indicates transformation of correlated FR and ellipticity noises to uncorrelated ones.

Figure 2

(a) Schematic of the experimental setup. The inset shows two possible magnetic field geometries (fixed direction $\mathit{B}$ or fixed amplitude rotating ${\mathit{B}}^{\prime }$). Panel (b) shows magnetic-field dependences of the FR noise (lower pictures) and examples of particular records of the FR and ellipticity noise spectra (upper plots) for the Nd-doped ${\mathrm{CaWO}}_4$ (b1) and ${\mathrm{LiYF}}_4$ (b2) crystals. (c) Orientational dependence of the FR noise spectra of the ${\mathrm{CaWO}}_4:{\mathrm{Nd}}^{3+}$ crystal. Magnetic field created by the permanent magnet was rotated in the plane normal to the laser beam. Both resonances follow the same orientational pattern. The low-frequency resonance presumably corresponds to the known tetragonal neodymium center (accentuated with a dotted line).